yehuda ben-shimol writes:
> As I remember, DiracDelta is singular and has a meaning only under
> integration. Anyway the properties of the DiracDelta are kept by
> Mathematica i.e., Integrate[(x - y)DiracDelta[x - y], {x, -1, 1},
> {y, -1, 1}] returns 0 as expected
Andrzej Kozlowski writes pretty much the same:
> On the one hand I think the Mathematica implementation of DiracDelta
> (and KroneckerDelta) leaves a lot to be desired... and that is putting
> it mildly. (That means I have plenty of much worse examples...).
>
> On the other hand, I am not convinced that Mathematica ought to perform
> this sort of simplification at all. DiracDelta is a generalised
> function. The statement x DiracDelta[x] == 0 needs a lot of
> interpreting to make sense of (I prefer to think of it as nonsense).
> However
>
>
> Integrate[(x-y) DiracDelta[x-y], {x,-Infinity,Infinity}]
>
> 0
>
> is correct.
I don't understand these reservations. I learned the statement x delta
= 0 in my lectures on distributions at university, and I checked today
that it also appears in one of Laurent Schwartz's ("father" of
distribution theory) books. Plus I find it very intuitive and it's
straightforward to demonstrate.
But anyway, I find in your responses the answer to my initial
questions, and I thank you for your time.
AC